I tried to use the instructions for installing Tensorflow on Ubuntu (1) to install on Debian Buster. The instructions say the Virtualenv option is simplest so I picked that. I'm not using a GPU. I did steps 1-4 on the referenced page, but step 5 ( pip3 install --upgrade tensorflow ) failed with several messages like:

That seems to find some of the stuff it needs, and generates some messages about collecting stuff, but in the end it too fails with similar retry messages followed by:

Could not find a version that satisfies the requirement werkzeug>=0.11.10 (from tensorboard<1.8.0->tensorflow==1.8.0) (from versions: )
No matching distribution found for werkzeug>=0.11.10 (from tensorboard<1.9.0,>=1.8.0->tensorflow

If I just retry it, it often fails with a different message, for example:

Could not find a version that satisfies the requirement html5lib==0.9999999 (from tensorboard<1.9.0,>=1.8.0->tensorflow) (from versions: )
No matching distribution found for html5lib==0.9999999 (from tensorboard<1.9.0,>=1.8.0->tensorflow)

or:

Could not find a version that satisfies the requirement markdown>=2.6.8 (from tensorboard<1.9.0,>=1.8.0->tensorflow) (from versions: )
No matching distribution found for markdown>=2.6.8 (from tensorboard<1.9.0,>=1.8.0->tensorflow)

An obvious alternative is to install from source as described here but something very similar happens on the very last step, which is